The trajectory of these numbers under iteration of sum of cubes of digits eventually turns out to be 371 or 407 (47 is the first of the second kind). - Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 19 2009

a(n-1), n >=1, is also the complex dimension of the manifold E(S), the set of all second order irreducible Fuchsian differential equations defined on P^1 = C U {oo}, having singular points at most in S = {a_1,..., a_n, a_{n+1}= oo}, a subset of P^1. See the Iwasaki et al. reference, Proposition 2.1.3., p. 149. - Wolfdieter Lang, Apr 22 2016